(573f) Inventory Routing in Industrial Gas Distribution

Authors: 
Dong, Y., University of Wisconsin-Madison
Maravelias, C. T., University of Wisconsin-Madison
Pinto, J. M., Linde plc
Granger, J., Praxair, Inc.



Many companies nowadays are trying to integrate various components of their supply chains (SCs) to achieve better performance. One example of such integration is in distribution logistics where “inventory control” is integrated with “transportation management”. Traditionally, customers place orders to the vendor, and then the vendor solves the distribution problem. Recently, many companies are adopting a Vendor Managed Inventory (VMI) policy, under which customers agree to let the vendor decide the re-supply time and amount, in essence, solve the inventory control problem for them. VMI generally allows vendors to plan their distribution activities according to current inventory levels and estimated consumption rates of customers, and it can be beneficial to both parties: for the vendor, it can significantly reduce the transportation cost by generating better distribution routes and schedules; for the customer, it reduces the resources necessary for inventory control and order placing. This integrated distribution problem is called Inventory Routing Problem (IRP), which is a very hard problem because inventory control, transportation routing, and scheduling are solved at the same time. Applications of IRP arise in various sectors, including gas, petrochemicals, chemical components, and suppliers of department stores. Since transportation cost is often a large fraction of the total SC cost, the efficient solution of IRP can lead to substantial efficiency, cost, and even environmental benefits.

To address this problem, we propose a systematic framework based on Mixed Integer Programming (MIP) models for IRP, as well as solution techniques. Cases from an industrial gas company (Praxair) are studied, but the model and solution methods can be used to address IRP problems in a wide range of sectors.

First, we introduce a general but flexible MIP model for the basic IRP, where both the inventories of the customers and the availabilities of trucks are considered. In this model, many realistic requirements can be modeled, including different tank capacities and trailer pumping rates, different access hours of customers, time-variant consumption rates, truck-customer compatibilities, and some special requirements from certain customers which still place orders in the traditional way, or need to be served first in a route. To address the challenge of driver requirements in truck-based transportation, we also present an extended model, which accounts for the availabilities and activities of drivers in detail, and satisfies the maximum working hour requirements. In addition, some preliminary work on solution methods, aiming to reduce the computational cost of solving MIP models, is presented, including preprocessing, valid inequalities and decomposition. Preprocessing of some redundant binary variables is used to reduce complexity of IRP instances, while valid inequalities based on customer/truck capacities and customer demands are developed to speed up the solution process. A decomposition method is also discussed, in which vehicle routes are firstly generated, and after that detailed trips with driver assignments are scheduled. Finally, since reducing the computation complexity without affecting the solution quality is of great importance, we discuss some other solution methods, including clustering and terminal constraints.